On the accuracy of Reissner-Mindlin plate model for stress boundary conditions

Zhang, Sheng

ESAIM: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 2, pp. 269-294.

For a plate subject to stress boundary condition, the deformation determined by the Reissner-Mindlin plate bending model could be bending dominated, transverse shear dominated, or neither (intermediate), depending on the load. We show that the Reissner-Mindlin model has a wider range of applicability than the Kirchhoff-Love model, but it does not always converge to the elasticity theory. In the case of bending domination, both the two models are accurate. In the case of transverse shear domination, the Reissner-Mindlin model is accurate but the Kirchhoff-Love model totally fails. In the intermediate case, while the Kirchhoff-Love model fails, the Reissner-Mindlin solution also has a relative error comparing to the elasticity solution, which does not decrease when the plate thickness tends to zero. We also show that under the conventional definition of the resultant loading functional, the well known shear correction factor $5/6$ in the Reissner-Mindlin model should be replaced by $1$. Otherwise, the range of applicability of the Reissner-Mindlin model is not wider than that of Kirchhoff-Love’s.

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